Eagles soar, hummingbirds whir. How a bird flies depends largely on how big the bird is. Likewise, hummingbird-sized aerial surveillance and reconaissance drones cannot depend on the same wing configurations and aerodynamics as their eagle-sized counterparts. As aerial vehicles become progressively smaller, the viscosity of the air takes on a greater importance (see “All About Eddy”). The ratio of the vehicle’s inertial force (propelling it forward) to the viscous force of the air (holding it back) decreases. To keep a tiny vehicle airborne on just the amount of fuel that it can carry requires wings that can generate the most lift with the least drag.

AHPCRC researchers Professor Antony Jameson (Stanford University, Aeronautics and Astronautics) and his student Matt Culbreth are using massively parallel high performance computing simulations to optimize airfoil shapes and to identify the attainable performance limits for a given vehicle size and configuration. For a given amount of lift, the computations test various shapes to see which shapes produce the least amount of drag. By using computational models, the researchers can test a large number of vehicle designs much more rapidly than if they had to generate physical prototypes for each design.

The Stanford researchers are performing their calculations using low values (1000 to 10,000) for the ratio of inertial to viscous forces, called the Reynolds number. Culbreth and Jameson have generated several airfoil configurations using a small number of geometry control points. Their work has produced airfoil geometries corresponding to a given pressure distribution, and they have successfully found the minimum amount of drag for a fixed lift coefficient.

The AERO-F simulation code that they use is massively parallel; that is, it runs on computer systems in which the work is distributed across many individual nodes. Each node consists of at least one processor, its own memory, and a link to the network that connects all the nodes together. The largest supercomputers have several hundreds of thousands of nodes in the same “box,” but parallel systems can also consist of clusters of conventional computers linked in such a way that they pass information back and forth as seamlessly as a single supercomputer. AERO-F is also scalable, making it possible to run equally well on systems of various sizes.

Computer simulations have already identified promising airfoil shapes that run counter to an engineer’s normal intuition—and that Nature never thought of. Camber (the difference in curvature between the top and bottom surfaces of an airfoil) can be optimized to reduce drag or to increase the angle at which the aircraft begins to stall. If the curvature is greater on the top surface, the camber is positive, while a greater curvature on the bottom surface produces negative camber—a configuration known as a supercritical airfoil shape, which has been used to improve the lift-to-drag ratio for high-speed aircraft.

Micro aerial vehicles are typically built for miniaturization rather than speed, and flapping wings are a necessity to generate enough lift to remain aloft. Simulations have identified combinations of flapping frequency and amplitude that do—and don’t—generate sufficient lift. The simulations show a trail of vortices behind the flapping wing, which can either help the vehicle (or bird) stay aloft or hinder it. (See next article for more about this work.)

Recent work is moving toward a 3D unsteady optimization of flapping motions for hovering and forward flight. The goal is to couple an advanced computational fluid dynamics code such as AERO-F with the optimization libraries developed elsewhere in AHPCRC in order to synthesize wing motions and deformations that optimize a specific performance metric.

Several iterations of a base mesh have been generated for the initial optimizations, incorporating refinements to improve accuracy, convergence, and resolution of flow features, while attempting to minimize the computational cost as much as possible. (See previous article for more about meshing schemes.)

The appropriate solver parameters are being determined for the AERO-F code running unsteady simulations at Reynolds numbers between 1,000 and 10,000. This process involves determining how to automate flow solutions and the post-processing of results so that they can be integrated with the optimization codes. At present, simulations involving wing pitching and plunging are being prepared to assess the trade-offs between mesh density and the ability to capture vorticity.

Source: AHPCRC Bulletin, Vol. 1, Issue 3 (2009)